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PreprintarXiv licencearXiv

Long interfacial internal waves with currents: current profiles with quadratic depth-dependence

  • Conor T. Curtin
  • Rossen I. Ivanov
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Abstract

Internal waves often propagate in the presence of currents. Internal waves and currents are widespread in the world's oceans. The equatorial internal waves and the equatorial undercurrent (EUC) are perhaps the most representative illustration of this phenomenon. The current profile in this study is a quadratic function of depth, which is in agreement with the known results of the EUC. With this assumption the integrable nonlinear Gardner's equation is derived as a model for the wave motion of the thermocline, separating the two layers of slightly different densities. In addition, we derive the generalised Gardner's equation in the case of variable bottom. We demonstrate that the coefficients of the equation are very sensitive with respect to the parameters of the EUC.

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Cite

BibTeXRIS
BibTeX
@misc{curtin2026long,
  title = {{Long interfacial internal waves with currents: current profiles with quadratic depth-dependence}},
  author = {Conor T. Curtin and Rossen I. Ivanov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10820},
  eprint = {2609.10820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10820},
}
RIS
TY  - UNPB
TI  - Long interfacial internal waves with currents: current profiles with quadratic depth-dependence
AU  - Conor T. Curtin
AU  - Rossen I. Ivanov
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10820
UR  - https://arxiv.org/abs/2609.10820
AB  - Internal waves often propagate in the presence of currents. Internal waves and currents are widespread in the world's oceans. The equatorial internal waves and the equatorial undercurrent (EUC) are perhaps the most representative illustration of this phenomenon. The current profile in this study is a quadratic function of depth, which is in agreement with the known results of the EUC. With this assumption the integrable nonlinear Gardner's equation is derived as a model for the wave motion of the thermocline, separating the two layers of slightly different densities. In addition, we derive the generalised Gardner's equation in the case of variable bottom. We demonstrate that the coefficients of the equation are very sensitive with respect to the parameters of the EUC.
ER  -